A corner shop fridge holds 40 chilled drinks: 14 apple, 11 orange and the rest lemon. One drink is taken at random. Find the probability that it is a lemon ...
Question 1 Report
A corner shop fridge holds 40 chilled drinks: 14 apple, 11 orange and the rest lemon. One drink is taken at random.
Find the probability that it is a lemon drink. (2)
Answer Details
Probability with equally likely outcomes is the number of favourable outcomes divided by the total number of outcomes. Every drink is equally likely to be taken, so the total is the \(40\) drinks in the fridge.
The lemon drinks are what is left once the other two flavours are removed:
\[40 - 14 - 11 = 15 \text{ lemon drinks}\][1]
\[P(\text{lemon}) = \frac{15}{40} = \frac{3}{8}\][1]
Both parts of the fraction divide by \(5\), giving the simplified form.
The denominator must be the total number of drinks, not the number of flavours, since the selection is made from the drinks. As a check, the three probabilities \(\frac{14}{40}\), \(\frac{11}{40}\) and \(\frac{15}{40}\) add to \(1\), which they must because the drink taken has to be one of the three flavours.
A probability of \(\frac{3}{8}\) is \(0.375\), a little over a third, which is reasonable given that lemon is the most common of the three.
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